Tone describes the author’s attitude toward his/her subject.
Tone has more to do with the author than what is happening in the text. The author is writing for a specific audience, and the tone suggests how the author feels about what he/she is writing about. For example, the tone of the author could be angry, sarcastic, formal, or serious.
Mood is the situation's atmosphere or characters' feelings.
The mood has to do with the feeling in the text. This is not the way the author feels, but the way the characters feel. For example, a character could be feeling nervous, joyful, angry, or loving. The mood also reflects the atmosphere, or how the situation feels. For example, a situation could be tense, traumatic, dramatic, or sad.
An example of mood could be if a character is about to get into a fight. The character may be feeling anxious or jumpy (character's mood), and the situation can be described as tense because anything could happen (atmosphere).